[ A g l ~values, and indicates no interference except a t very high concentrations. The analysis system, therefore, is not completely specific for sulfur groups but is highly selective because of the nature of the electrode and reagent system used.
DISCUSSION The continuous-flow system described has allowed the development of a simple, rapid method for determination of protein concentrations, apparently dependent on the disulfide content of the protein. The proposed method is a considerable improvement over the manual method described previously ( 5 ) . Some information about the stoichiometry of the reaction can be deduced from the data given in Figures 7-11. Because of the high selectivity of the electrode for thiol groups (20), the reaction must certainly involve rupture of disulfides giving a thiol product capable of strongly complexing silver ion. The slope of the plot in Figure 9 showing the effect of hydroxide ion on potential indicated a 1:l stoichimetry between Agt and OH- as the extent of disulfide splitting was increased. The reaction can therefore be written similarly to the stoichiometry determined by Cecil and McPhee (21) for low molecular weight disulfides:
P-(SS),-P + xAg+ + xOH- +P(SAg)x
+ P(SOH), (1)
where X is the number of disulfide groups in the protein. The slopes of the calibrations in Figure 7, 8, 10 and 11 should then depend on the number of x, but will also be influenced by the factors mentioned in the Result Section, the equilibrium constants for complexing of silver by the reagent substrate, and by the presence of free S H groups in the protein. This is an extremely complicated situation and direct information about x cannot be easily obtained from these data. However, the electrode response is a t least semiquantitatively related to the number of disulfide groups in the protein, as shown in Figure 11. BSA and HSA both contain 17 SS groups per molecule (15) with molecular (20) G A RechnitzandT M Hseu Ana/ Chem 40, 1054 (1968) ( 2 1 ) R Cecil andJ R McPhee Biochem J 66, 538 (1957)
weights of 66,000 and 69,000, respectively, while 7-G contains only 12 SS bonds/molecule for a molecular weight of 160,000 (18).In principle, it should be possible to use the AgzS electrode directly to monitor protein breakdown without the addition of silver ion. However, in practice it is found that electrode response is too sluggish to permit effective monitoring a t low protein concentration levels unless silver ion is added to the solution. Interference effects have been shown to be minimal in Table V. Expected interferences from ammonia and urea are negligible a t respective concentrations of 10T3M and 10-lM. For 0.1 mg/ml BSA, it would be expected that one could tolerate ratios of ca. lo3 and lo5 of ammonia and urea in excess before interference occurred. These high selectivities can be attributed to the very high stability constant of silver thiol complexes in comparison to nitrogen donor complexes (19). The method suffers from the fact that different proteins give a different response depending on protein structure, as in some colorimetric methods ( 6 ) , but possesses a number of advantages over these methods because of the use of the electrode sensing system. The instrument cost is low; the method is virtually specific for sulfur-groups and interferences common in the Lowry and biuret methods cannot occur. Sensitivity in the range 5-100 pg/ml compares favorably to the Lowry method (8, 13), and the sensitivity of response can be varied simply by changing total silver ion concentration. Linear response is obtained over a wider concentration range than Hartree’s (13) modified Lowry method and the method requires only 2-minute mixing time as compared to 30 minutes for the biuret and Lowry methods. Despite the variation in response for different proteins, these advantages should allow wide application in biological studies, including sensing for column chromatography and immunochemical separations, and determination of protein-sulfur content of biological fluids. Presumably, the sensitivity could be still further improved by miniaturization of the manifold, improved electrode flow-through design and increasing the length of time for reaction. Received for review December 3, 1973. Accepted February 19, 1974. Financial support by the National Institutes of Health is gratefully acknowledged.
Digital Simulation of a Rotating Photoelectrode Photolysis of Benzophenone in Aklaline Media J. R. Lubbers,’ E. W. Resnick,2 P. R . Gaines, and
D. C. Johnson3
Department of Chemistry, Iowa State University. Ames, lowa 50070
A program is described for the digital simulation of convective-diffusional mass transport, photolytic and homogeneous chemical processes, and electrochemical reaction of the photoproducts at a rotating photoelectrode. The simulation required use of expanded equations for axial and radial convection. A rotating photoelectrode and results of the simulation were applied in a kinetic study of the photodimerization of benzophenone in alkaline alcohol-water solutions. The rate constant determined is in agreement with literature values determined by independent methods.
Rotating ring-disk electrodes (RRDE) have been demonstrated to be useful for the study of mechanisms of electrochemical processes and the kinetics of homogeneous reactions involving the products of electrochemical reactions. The applicability results because the rate of mass transport a t the electrode can be easily controlled, reactive intermediates with a large range of half-lives can be Present address. Department of Chemistry, Ohio State University, Columbus, Ohio 43201. Present address, Microswitch, Freeport, Ill. 61032. Author to whom correspondence should be sent. A N A L Y T I C A L C H E M I S T R Y , VOL. 46, N O . 7, J U N E 1974
865
........ ...
~.
.I
mirror
to phatoelectrode
..... .....
8
,
0
d
;:
S O Y ~ C Ca
rc
mirror
Optical diagram of instrumental system for use with the rotating photoelectrode Figure 1.
detected, the hydrodynamic profiles a t the rotating electrode are accurately known, and the equation of convective-diffusional mass transport has been solved for many kinetic situations. The theory and application of the RRDE were recently given excellent review by Albery and Hitchman ( I ) . We recently described a rotating photoelectrode for electrochemical studies of the products of photochemical reactions in liquid media (2). The design of the photoelectrode was inspired by that of the RRDE and is shown in Figure 1 of Reference 2. The electrode consists of an optically transparent quartz disk surrounded by and in the same plane of annular platinum electrode. The metallic cylinder on which the annular electrode is mounted is encased in a Teflon shroud having its end-surface in the plane of the ring electrode and the quartz disk. In use, the photoelectrode is rotated about an axis perpendicular to and passing through the center of the quartz disk. A beam of light collimated parallel to the axis of rotation is directed through the quartz disk. Products of photolytic processes generated in the vicinity of the quartz disk are transported by convective-diffusional processes to the surface of the ring electrode where they may undergo electrochemical reaction. The photocurrent in the ring electrode is a function of the following parameters: intensity of the light beam; molar absorptivity and concentration of the absorbing species; quantum efficiency of the photolytic process; mechanism and rate of chemical reactions involving products of the photolytic process; and angular velocity of electrode rotation. To obtain a quantitative relationship between photocurrent and the parameters above, it is necessary to solve the equation of convective-diffusional mass transport in cylindrical coordinates.
ac - +
ac + ar
ur-
ac
uX-
=
a2c
(3)
(4)
The value of pK, for the protonated free-radical intermediate is 9.2 (9). The rate constant, k , was determined by Beckett and Porter to be 1.1 x 109M-l sec-l in 1:l isopropanol-water (9). The protonated free radical, HR, and radical anion, R - , cannot be distinguished electrochemically a t the ring electrode of the RPE. They are both oxidized by one-electron processes to benzophenone, A. The photocurrent is a measure of the sum of the concentrations of HR and R- , C,, a t the surface of the ring electrode.
CB
=
[HR]
+ [R-]
(5)
The rate of dimerization expressed in terms of CB is
D , ax
at ax where C = concentration variable, ur = fluid velocity vector along the radial coordinate, u x = fluid velocity vector along the axial coordinate, t = time, and D = diffusion coefficient. Because of angular symmetry, all derivatives with respect to the angular coordinate are zero. Radial diffusion is negligible as a means of mass transport in comparison to radial convection ( I ) . (1) W . J. Albery and M. L. Hitchman, "Ring-Disc Electrodes," Clarendon Press, Oxford, 1971 (2) D. C. Johnson and R. W. Resnick, Anal. Chem., 44,637 (1972).
866
An exact description of the hydrodynamics at a rotating surface such as the RPE was given (3-5), and the velocity vectors were expressed as power series. Closed-form mathematical solutions to Equation 1 have been given for the rotating disk electrode (RDE), rotating ring electrode (RRE), and rotating ring-disk electrode (RRDE) ( I , 5 ) . In these derivations, U r and u x were accurately expressed by the first term in the respective power series since all electrochemical and homogeneous chemical reactions a t these electrodes occur in a very thin layer of fluid a t the electrode surface. I t is not expected that a closed-form mathematical solution to Equation 1 will be obtained for the W E because the light beam penetrates the fluid adjacent to the optical disk a t a distance much greater than treated for the RDE, RRE, and RRDE. The full power series must be used to describe convection a t these large distances. A general approach for obtaining numerical solutions to Equation 1 was described by Feldberg (6) for the RDE and was expanded by Prater and Bard ( 7 ) for the RRDE. Because of the success of their calculations and the obvious similarities between the RPE and the RRDE, we have extended the principles of digital similation to the RPE. Here we describe the digital program and its application to a kinetic study of the photopinacolization of benzophenone in strongly alkaline, alcohol-water solutions. The mechanism for the reaction has been established to be that shown in Equations 2-4 (8, 9). OH
A N A L Y T I C A L CHEMISTRY, VOL. 46, NO. 7, JUNE 1974
(3) Th. von Karrnon, Z.Angew. Math. Mech., 1, 233 (1921). (4) W. G. Cochran, Proc. Cambridge Phil. SOC.,30, 365 (1934). (5) V. G . Levich, "Physicochemical Hydrodynamics," Prentice-Hall, Englewood Cliffs, N.J.. 1962. (6) S. W. Feldberg. "Electroanalytical Chemistry," Vol. 3, A. J. Bard. Ed., Marcel Dekker, New York, N.Y.. 1969. (7) K. B. Prater and A. J. Bard, J. Electrochem. Soc., 117, 207 (1970). (8) G. Porter and F. Wilkinson, Trans. FaradaySoc., 57, 1686 (1961). (9) A. Beckett and G. Porter, Trans. Faraday SOC., 59, 2038, 2051 (1963)
-2k [HR] [R-] where [HR] = and
tion. Thus, any annular box in the array of volume elements can be designated by the set of integers (J, K ) . The value of Ar is chosen so that the various radii of the RPE are satisfactorily approximated by integral numbers of concentric boxes. R,
[R-] = Thus
In strongly alkaline solutions, [H+] > 0.0, I h v increases as w is increased since the rate of radial transport increases with w allowing less time for the chemical reaction of the intermediates. Unexpected is the prediction that for XK = 0.0, Ihv is largest for the lowest value of w . This dependence probably results because, near the surface of the electrode, the rate of radial transport increases more rapidly than the rate of axial transport as w is increased; compare Equations 24 and 25 and plots of H and Fl in Reference 5. Hence, species generated photolytically at a finite distance from the surface of the quartz disk are transported to the ring electrode a t low w but are swept clear of the ring surface at high w . This dependence of Ihv on w at XK = 0.0 has not yet been tested experimentally.
2.0
1
1.0
c
4
R o t a t i o n a l V e l o c ~ ~( ryo d / s a c l
Figure 4. XI1
= 6.0
/hv VS.
rotational velocity
X 10'4quanta/sec, CBULKA
= 0.010M,
[NaOH] = 1.OM
Values of XK for the benzophenone system were calculated from experimental data using observed values of Ihv and the smooth curves fitting the simulated data in Figure 3. Results are given in Table I1 for 0.10M NaOH and inTable I11 for 1.OMNaOH. Results of repeated determinations for 0.1OM NaOH were scattered comparable to data in Table 11. The high precision of XK values in Table I11 as compared with Table 11 results partly from the greater sensitivity of Ihv A N A L Y T I C A L C H E M I S T R Y , VOL. 46, N O . 7, J U N E 1974
871
32;
3-
28-
I
i
14-
-
6-
i
_--PI 1
4’
,‘
~
-m-
~
w’ 9 -
I
2
3
xII
I
IO-“
12
8
4
I6
20
24
I
,
C B U L K A “ 1 0 ’ (t.j)
S
4
6
Figure 7.
/hv
lquonto/recl
XI1 = 6.0 X
Figure 5. /hu vs. XI I
vs. CBULKA loi4
quanta/sec; values of XK:
- - - O.OM-’
s e c - ’ and
3.7 x i 0 5 M - ’ sec-1. , values of w: (0) 41.9 rad/sec, ( A ) 94.3rad/sec. and ( 0 )167.7radjsec; (x) experimental ~
CBULKA = 0.010M. w = 4 1 . 9 rad/sec; values of XK: O.OM-’ s e c - ’ . - - - 1 . 2 X 105M-’ sec-’, and ___ 3.7 x i o % - ’ s e c - I ; ( 0 )simulated and (e)experimental -.-e-
Profiles of Lighl Intensity a1 O u a r t r D i s k T a k e n
at Right Angler
10k
Diatance (arbitrary units)
Figure 8. Light intensity profiles
4-
Measured along perpendicular diameters 2-
I
2
3 XII X I O - ’ ‘
4
5
6
(quanfo/sec)
Figure 6. /hu vs. XI1 CBULKA = 0 OlOM, w = 94 3 rad/sec; values of XK 0 OM-’ sec-’, - - - 1 . 2 x 1 0 5 ~ 4 - lsec-’, and ___ 3 7 x i 0 5 M - ’ s e c - ’ , ( A )simulated and ( a )experimental -.-e-
to change in XK in that region of the simulation. Our values of the observed rate constant are in good agreement with literature values. The values of fhu observed for the two largest values of w in 1.OM NaOH (Table 111) are identical and correspond to the point of intersection of simulated curves for those values of w in Figure 3. This is supporting evidence for the correctness of the program and the predicted inversion of 872
* ANALYTICAL CHEMISTRY, VOL.
46, NO. 7 , JUNE 1974
w-dependency as a function of decreasing XK. Thorough consideration of the results shown in Figure 3 leads to the conclusion that for any finite value of XK, a recording of Zhv us. w will be characterized by a maximum. An increased value of XK will result in a shift of the maximum toward a high value of w . Figure 4 contains a plot of Ihu us. w for 1.OM NaOH. The maximum exists a t w = 200 rad/ sec. No digital simulation of the data in Figure 4 was performed. The broadness of the maximum probably prevents accurate diagnostic application of this phenomenon for evaluating XK. Simulation of Ihyus. XII. Simulated values of Ihv as a function of XI1 for XK = 0.0, 1.2 x lo5, and 3.7 x 105 M - l sec-1 are shown plotted in Figure 5 for w = 41.9 rad/ sec and in Figure 6 for w = 94.3 rad/sec. Experimental results are also plotted and the agreement between experimental and simulated data is good. The observation is in-
teresting that a t XK = 0.0 M - l sec-l, I h y is simulated to be a linear function of XII. No experimental confirmation of this correspondence has as yet been made. Simulation of &, us. CBULKA. Simulated values of Ih, are shown plotted in Figure 7 for XK = 0.0 and 3.7 x 105 M - l sec-'. Also shown are values obtained experimentally. The agreement between experimental and simulated data is good. Light Intensity Profile. Uniformity of light intensity was assumed across the surface of the quartz disk for development of the digital program. The assumption permitted simplification of the calculations of mass transport and photochemical reaction in the zone of the quartz disk (r 5 R1) in that dCH/dr = 0. Two intensity profiles taken on perpendicular diameters across the surface of the quartz disk are shown in Figure 8. These profiles demonstrate that the assumption of uniform intensity is not strictly valid. The effect of the incorrect assumption is that experimental values of XK are too large, particularly a t low values of w . This follows since the rate of photochemical generation of electroactive intermediate near the outer edge of the zone of the quartz disk is actually less than the rate simulated. At low values of w , the main source of a chemically reactive electroactive intermediate reaching the surface of the ring electrode is the outer edge
of the zone of the quartz disk. Lack of funds prevented digital simulation based on measured intensity profile and the magnitude of error produced by the assumption has not been evaluated a t this time. CONCLUSIONS The experimental result of the determination of the rate constant for the photopinacolization of benzophenone in alkaline media is in good agreement with the literature values. The experimentally observed dependence of photocurrent on angular velocity of electrode rotation, light intensity, and bulk concentration of benzophenone are in excellent agreement with the simulated results. These findings Confirm the accuracy and applicability of the simulation program for interpretation of the results obtained using a rotating photoelectrode. ACKNOWLEDGMENT The authors are grateful to Val Peacock for assistance in experimentation. Received for review August 27, 1973. Accepted December 21, 1973. The authors are grateful for financial support of this research by Research Corporation and National Science Foundation (GP-18575).
Study of the Behavior of Copper Ion-Selective Electrodes at Submicromolar Concentration Levels W. J. Blaedel and D. E. Dinwiddie Department of Chemistry, University of Wisconsin, Madison, Wis. 53706
The behavior of a copper ion-selective electrode is investigated in the range 10-6-10-9M of copper ion. After cleaning by immersion in dilute H2S04, the potential response changes toward its equilibrium potential upon immersion in dilute C u ( l l ) solution. The rate of change of potential is dependent upon the copper ion concentration. EDTA interferes, but 1 0 - 5 M concentrations of H+, C a 2 + , Z n 2 + , AI3+, and Fe3+ interfere only slightly at the 10-7M level of copper ion. Possible analytical use for quantitation purposes is described.
The limit of detection of cupric ion activity in noncomplexing solutions using CuS-Ag2S cupric ion-selective electrodes is given in the literature as 10-8M ( I ) . This limit of detection is far too high to be explained by simple mechanisms involving the solubility of CuS and Ag2S alone. The same type of discrepancy is observed regarding the high limit of detection of silver ion or sulfide ion using the AgzS ion-selective electrode (J. W. Ross, p 57, Ref. 2 ) . Even when the hydrogen sulfide equilibria are taken into account a t pH 6, the solubility of CuS from the sensing electrode is calculated t o be around 10- 14M, far below the observed limit of 10--sM. In solutions which contain rela(1) Orion Research Inc.. Instruction Manual, Cupric ion Electrode Model 94-29 (1968) (2) R A . Durst. E d . , "Ion-Selective Electrodes," N a t . Bur. Stand. ( U S ) , Spec. Pub/. 314, 1969
tively large concentrations of complexing agents, potentials corresponding to free cupric ion activities as low as W20M are observed ( I ) . Such low activities are a t variance with the value of 10-sM observed in uncomplexed systems, and no satisfactory explanation of these discrepancies seems to have been given in the literature to date. In this paper, exploratory experiments and tests are presented on some factors which affect the response of a copper ion-selective electrode to submicromolar concentration levels of copper ion. Based on this work, an explanation is proposed to account for the electrode response in systems containing low concentrations of copper ion. The possible analytical usefulness of the ion-selective electrode for the measurement of submicromolar concentrations of copper ion is explored.
EXPERIMENTAL Apparatus. A commercial cupric ion-selective electrode and a single junction silver-silver chloride reference electrode (Model Nos. 94-29 and 90-01, Orion Research, Cambridge, Mass.) were used in all experiments. The electrode leads were connected to a Leeds and Korthrup specific ion millivolt meter (Model 7410). A Sargent Model SR recorder was used to record the meter output. All potential readings were made on solutions thermostated at 25 f 0.1 "C in a water bath (Model MR-3220A-1, Blue M Electric Company, Blue Island, Ill. ). Reproducible stirring was achieved by mounting the electrodes on a motor-driven holder arm which moved the electrodes back and forth through the solution over a l%inch path length at about 90 cycles per minute. A N A L Y T I C A L C H E M I S T R Y , VOL. 46, N O . 7 , JUNE 1974
873
